Effective Carrier Sensing in CSMA Networks under Cumulative Interference

Transcription

1 Effective Carrier Sensing in CSMA Networks under Cumulative Interference Liqun Fu, Member, IEEE, Soung Chang Liew, Fellow, IEEE, and Jianwei Huang, Senior Member, IEEE Abstract This paper proposes the concept of safe carrier-sensing range under the cumulative interference model that guarantees interference-safe (also known as hidden-node-free) transmissions in CSMA networks. Compared with a previous related concept of safe carrier-sensing range under the commonly assumed but less realistic pairwise interference model, we show that the safe carrier-sensing range under the cumulative interference model is larger by a constant multiplicative factor. For example, the factor is.4 if the SINR requirement is 0dB and the path-loss exponent is 4 in a noiseless case. We further show that the concept of a safe carrier-sensing range, although amenable to elegant analytical results, is inherently not compatible with the conventional power-threshold carrier-sensing mechanism (e.g., that used in IEEE 80.). Specifically, the absolute power sensed by a node in the conventional carrier-sensing mechanism does not contain enough information for the node to derive its distances from other concurrent transmitting nodes. We show that, fortunately, a new carrier-sensing mechanism called Incremental-Power Carrier-Sensing (IPCS) can realize the carrier-sensing range concept in a simple way. Instead of monitoring the absolute detected power, the IPCS mechanism monitors every increment in the detected power. This means that IPCS can separate the detected power of every concurrent transmitter, and map the power profile to the required distance information. Our extensive simulation results indicate that IPCS can boost spatial reuse and network throughput by up to 60% relative to the conventional carrier-sensing mechanism under the same carrier-sensing power thresholds. If we compare the imum throughput in the interference-free regime, the throughput improvement of IPCS is still more than 5%. Last but not least, IPCS not only allows us to implement the safe carrier-sensing range, but also ties up a loose end in many other prior theoretical works that implicitly used a carrier-sensing range (interference-safe or otherwise) without an explicit design to realize it. Index Terms carrier-sensing range, cumulative interference model, CSMA, WiFi, IEEE 80., SINR constraints, spatial reuse. INTRODUCTION AND OVERVIEW Due to the broadcast nature of wireless channels, signals transmitted over wireless links can mutually interfere with each other. Optimizing spatial reuse and network throughput under such mutual interferences has been an intensely studied issue in wireless networking. In particular, it is desirable to allow as many links as possible to transmit together in an interference-safe (or collision-free) manner. The problem of interference-safe transmissions under the coordination of a centralized TDMA (Time-Division Multiple-Access) scheduler has been well studied (e.g., see [] [7]). Less well understood is the issue of interference-safe transmissions under the coordination of a distributed scheduling protocol. Liqun Fu is with the Institute of Network Coding, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong. lqfu@inc.cuhk.edu.hk. Soung Chang Liew and Jianwei Huang are with the Department of Information Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong. s:{soung,jwhuang}@ie.cuhk.edu.hk. An earlier version of this paper appeared in the proceedings of IEEE INFOCOM 00 []. This work is supported by AoE grant E-0/08 from the UGC of the Hong Kong SAR, China, the General Research Funds (Project Number 45 and 449) established under the University Grant Committee of the Hong Kong Special Administrative Region, China. The CSMA (Carrier-Sense Multiple-Access) protocol, such as IEEE 80., is the most widely adopted distributed scheduling protocol in practice. As the growth of 80. network deployments continues unabated, we are witnessing an increasing level of mutual interference among transmissions in such networks. It is critical to establish a rigorous conceptual framework upon which effective solutions to interference-safe transmissions can be constructed. Within this context, this paper has three major contributions listed as follows (more detailed overview is given in the succeeding paragraphs): ) We propose the concept of a safe carrier-sensing range that guarantees interference-safe transmissions in CSMA networks under the cumulative interference model. ) We show that the concept is implementable using a simple Incremental-Power Carrier- Sensing (IPCS) mechanism. ) We demonstrate that implementation of the safe carrier-sensing range under IPCS can significantly improve spatial reuse and network throughput as compared to the conventional absolute-power carrier-sensing mechanism. Regarding ), this paper considers the cumulative interference model (also termed physical interference Digital Object Indentifier 0.09/TMC //$.00 0 IEEE

2 model in [8]), in which the interference at a receiver node includes the cumulative power received from all the other nodes that are currently transmitting (except its own transmitter). This model is more realistic, but is much more difficult to analyze than the widely studied pairwise interference model (also termed the protocol interference model in [8]) in the literature. Under the cumulative interference model, a set of simultaneously transmitting links are said to be interference-safe if the SINRs (Signal-to-Interferenceplus-Noise Ratios) at these links receivers are above a threshold. Given a set of links L in the network, there are many subsets of links, S L, that are interference-safe. The set of all such subsets F = {S the SINRs of all links in S are satisfied} constitutes the feasible interference-safe state space. For centralized TDMA, all subsets are available for scheduling, and a TDMA schedule is basically a sequence (S t ) n t= where each S t F. For CSMA, because of the random and distributed nature of the carrier-sensing operations by individual nodes, the simultaneously transmitting links S CS may or may not belong to F. Let F CS = {S CS simultaneous transmissions of links in S CS are allowed by the carrier-sensing operation}. The CSMA network is said to be interference-safe if F CS F. This is also the condition for the socalled hidden-node free operation [9]. However, this issue was studied under the context of an idealized pairwise interference model in [9] rather than the practical cumulative interference model of interest here. In this paper, we show that if the carrier-sensing mechanism can guarantee that the distance between every pair of transmitters is separated by a safe carriersensing range, thenf CS F can be guaranteed and the CSMA network is interference-safe even under the cumulative interference model. The safe carriersensing range established in this paper is a tight upperbound and achieves good spatial reuse. Given the above result, the next important issue to address is how to implement a carrier-sensing mechanism such that every pair of simultaneous transmitting nodes is separated by the targeted carrier-sensing range. This brings us to ) above. In the conventional carrier sensing based on a power threshold (e.g., that of the basic mode in IEEE 80.), each transmitter monitors the absolute power received. This power consists of the sum total of powers received from all the other transmitters. It is impossible to infer from this absolute power the exact separation of the node from each of the other transmitters. This is thus not compatible with the concept of safe carriersensing range, and leads to poor spatial reuse. To address this, we propose a simple mechanism that monitors the incremental power changes over time, IPCS, which enables us to map the power profile to the required distance information. We believe that this mechanism, although simple, has a significant contribution as it shows that the theoretical concept of safe carrier-sensing range can be implemented rather easily in practice. It also ties up a loose end in many other prior theoretical works that implicitly assume the use of a carrier-sensing range (interference-safe or otherwise) without an explicit design to realize it. That is, IPCS can be used to implement the required carrier-sensing range in these works, not just our safe carrier-sensing range here. Given the implementability of a safe carrier-sensing range, the next issue is how tight the simultaneously transmitting nodes can be packed. This brings us to ) above. In the conventional carrier-sensing mechanism, to ensure that the detected absolute power is below the carrier-sensing power threshold, the separation between a newly active transmitter and other existing active transmitters must increase progressively as the number of concurrent transmissions increases. That is, the cost of ensuring interference-safe transmissions becomes progressively higher and higher in the packing process. This reduces spatial reuse and the overall network throughput. Fortunately, with IPCS, the required separation between any pair of active transmitters remains constant as the safe carriersensing range, and is independent of the number of concurrent transmissions. Indeed, our simulation results indicate that IPCS mechanism can improve the spatial reuse and the network throughput by up to 60% compared with the conventional carrier-sensing mechanism under the same carrier-sensing power thresholds. If we compare the imum throughput in the interference-free regime, the throughput improvement of IPCS is still more than 5%.. Related Work In the literature, most studies on carrier sensing (e.g., [9] [5]) are based on the pairwise interference model. For a link under the pairwise interference model, the interferences from the other links are considered one by one. If any two links can transmit concurrently without a collision, then it is assumed that there is no collision overall. Ref. [9] established the carrier-sensing range required to prevent hidden-node collisions in CSMA networks under the pairwise interference model. Ref. [4] studied the use of power control to increase network capacity again under the pairwise interference model. The resulting separations between transmitting nodes in [9] and [4] are overly optimistic and cannot eliminate hidden-node collisions if the more accurate cumulative interference model is adopted. A number of recent papers studied the CSMA networks under the cumulative interference model (e.g., [6] [9]). An earlier unpublished technical report of ours [6] derived the safe carrier-sensing range under the cumulative interference model. The technical report, however, did not include the IPCS realization presented in this paper. Neither did Ref. [7] [9] address the implementation of a carrier-sensing

3 Interference Models Absolute power carrier sensing Incremental power carrier sensing TABLE Summary of the Related Work Pairwise Interference Model many (e.g., [9], [0]) This paper Cumulative Interference Model [8], [9] This paper range based on power detection. Ref. [7] studied the asymptotic capacity of large-scale CSMA networks with hidden-node-free designs. The focus of [7] is on an order result rather than a tight result. For example, in the noiseless case where γ 0 =0dB and α =4, the safe carrier-sensing range derived in [7] is 8.75d. In this paper, we show that setting the safe carrier-sensing range to 5.7d is enough to prevent hidden-node collisions. The authors in [8], [9] attempted to improve spatial reuse and capacity by tuning the transmit power and the carrier-sensing range. Although the cumulative interference model is considered in [8], [9], spatial reuse and capacity are analyzed based on a carrier-sensing range. In particular, they assumed that the transmitters of concurrent transmission links can be uniformly packed in the network. As discussed in this paper, such uniform packing cannot be realized using the current 80. carrier-sensing mechanism. Therefore, the results in [8], [9] are overly optimistic without an appropriate carrier-sensing mechanism. IPCS fills this gap so that the theoretical results of [8], [9] remain valid. We summarize the key related models and results in the literature in Table. In this paper, we focus on 80. networks operating with the basic access mode. We do not consider virtual carrier sensing (i.e., the RTS/CTS mode). Ensuring interference-safe operation under virtual carrier sensing is rather complicated even under the pairwise interference model (see [] for details); when the cumulative interference model is considered, the use of RTS/CTS requires more modifications at the MAC layer of the 80. protocol in order to ensure interference-safe transmissions. SYSTEM MODEL. Cumulative Interference Model We represent links in a wireless network by a set of distinct and directed transmitter-receiver pairs L = {l i, i L }. Let T = {T i, i L } and R = {R i, i L }denote the set of transmitter nodes and the set of receiver nodes, respectively. A. This paper focuses on the incremental-power carrier-sensing (IPCS) mechanism under the cumulative interference model. But IPCS proposed in this paper can also deal with the pairwise interference model. receiver decodes its signal successfully if and only if the received Signal-to-Interference-plus-Noise Ratio (SINR) is above a certain threshold. We adopt the cumulative interference model, where the interference is the sum of the received powers from all transmitters except its own transmitter. We assume that radio signal propagation follows the log-distance path model with a path loss exponent α>. The path gain G(T i,r j ) from transmitter T i to receiver R j is: ( ) α d(ti,r j ) G(T i,r j )=G(d 0 ), where d(t i,r j ) is the Euclidean distance between nodes T i and R j, and G(d 0 ) is the reference path gain at the reference distance d 0 [0]. Without loss of generality, we assume d 0 =and use G 0 to denote the reference path gain at d 0 =. So the path gain G(T i,r j ) is d 0 G(T i,r j )=G 0 d(t i,r j ) α. In 80., each packet transmission on a link l i consists of a DATA frame in the forward direction (from T i to R i ) followed by an ACK frame in the reverse direction (from R i to T i ). The packet transmission is said to be successful if and only if both the DATA frame and the ACK frame are received correctly. Let L (L ) denote the set of links that transmit concurrently with the DATA (ACK) frame on link l i. Under the cumulative interference model, a successful transmission on link l i needs to satisfy the following conditions: P t G(T i,r i ) N + P t G(S j,r i ) γ 0, (DATA frame) () l j L and P t G(R i,t i ) N + P t G(S j,t i ) γ 0, l j L (ACK frame) () where P t is the transmit power, N is the average noise power, and γ 0 is the SINR threshold for a successful reception. We assume that all nodes in the network use the same transmit power P t and adopt the same SINR threshold γ 0. For a link l j in L (L ), S j represents the sender of l j, which can be either T j or R j. This is because both DATA and ACK transmissions on link l j may cause interference to link l i.. Existing Carrier Sensing Mechanism in 80. If there exists a link l i L such that not both () and () are satisfied, then there is a collision in the network. In 80., carrier sensing is designed to prevent such collisions. In this paper, we assume carrier sensing by energy detection. Consider a link l i. If transmitter T i senses a power P CS (T i ) that exceeds a power threshold P th, i.e., P CS (T i ) >P th, ()

4 4 then T i will not transmit and its backoff countdown process will be frozen. This will prevent the DATA frame transmission on l i. A proper choice of P th can prevent collisions without significantly reducing spatial reuse in the network.. Carrier-sensing Range Concept In most studies of 80. networks, the concept of a carrier-sensing range (CSR) is introduced. Consider two links, l i and l j. If the distance between transmitters T i and T j is no less than the carrier-sensing range, i.e., d(t i,t j ) CSR, (4) then it is assumed that T i and T j cannot carrier sense each other, and thus they can initiate concurrent transmissions on links l i and l j. The pairwise relationship can be generalized to a set of links S CS L. If condition (4) is satisfied by all pairs of transmitters in set S CS, then all links in S CS can transmit concurrently. The carrier-sensing range (and the corresponding power threshold used in the practical protocol design) is crucial to the throughput performance of CSMAtype networks. If CSR is too large, spatial reuse will be unnecessarily limited. If CSR is not large enough, then hidden-node collisions may occur, due to the violation of () or (). We now define a safe carriersensing range that always prevents the hidden-node collisions in 80. networks under the cumulative interference model: Definition (Safe-CSR cumulative ): Let S CS Ldenote a subset of links that are allowed to transmit concurrently under a carrier-sensing range CSR. Let F CS = {S CS } denote all such subsets of links in the network. A CSR is a safe carrier-sensing range under the cumulative interference model (denoted as Safe- CSR cumulative )ifforanys CS F CS and for any link l i S CS, both conditions () and () are satisfied, with L = L = S CS \{l i }..4 Mapping CSR to P th The carrier-sensing range concept is widely used to capture the carrier-sensing mechanism in 80. (e.g., [9] [4], [8], [9]). The carrier-sensing range describes the minimum distance requirement between every pair of transmitters of the links that can concurrently transmit. Therefore, the carrier-sensing range is a pairwise concept. However, the current energy-detection carrier-sensing mechanism in 80. compares the detected absolute power with a power threshold P th. The detected power consists of the sum total of powers received from all the other transmitters. From this absolute detected power, it is impossible for a node to infer the exact separation between it and each of the other transmitters. Thus, the concept of carrier-sensing range cannot be realized in a precise manner. In short, there is a gap between the pair-wise carrier-sensing range concept and the absolute power detection carrier-sensing mechanism. Nevertheless, if we really want to ensure that the separation between any pair of transmitters is no less than the carrier-sensing range CSR, the carriersensing power threshold P th can be set as: P th = P t G 0 (CSR) α. (5) This is, however, a very conservative way to set the power threshold. It makes use of the fact that if the aggregate power received from all transmitters is less than P th, then the power from any of the transmitters is less than P th. Hence, the minimum separation of CSR can be guaranteed. Effectively, we are treating the power sensed as the power from one individual transmitter only. For example, using the above power threshold, we observe that the separation between concurrent transmitters will increase progressively as more links join in the simultaneous transmissions (detailed explanation is in Section 4.). In other words, the carrier-sensing range concept cannot be implemented effectively with the current carrier-sensing mechanism. A consequence of this is that the spatial reuse is reduced unnecessarily. In this paper, we propose a new Incremental-Power Carrier-Sensing (IPCS) to fill the gap of effective implementation of the carrier-sensing range concept. In particular, setting the carrier-sensing power threshold as in (5) in IPCS allows precise implementation of the carrier-sensing range CSR (see Section 4 for details). SAFE CARRIER-SENSING RANGE UNDER CUMULATIVE INTERFERENCE MODEL In this section, we derive a sufficient condition for Safe-CSR cumulative. When discussing the hidden-node free design, it is required that the receivers are operated with the RS (Re-Start) mode.. The Need for RS (Re-Start) Mode It is shown in [9] that even when the carrier-sensing range is sufficiently large to satisfy the SINR requirements of simultaneous transmitting nodes, transmission failures can still occur due to the Receiver- Capture effect. Fig.. Collision due to Receiver-Capture effect Consider a two-link example shown in Fig., where d(t,t ) >CSRand d(t,r ) <CSR.Sothetransmitters T and T cannot carrier-sense each other, but

5 5 R can sense the signal transmitted from T. Suppose that CSR is set large enough to guarantee the SINR requirements on l and l (both the DATA frames and the ACK frames). If T transmits first, then R can sense the signal of T. The default operation in most 80. products is that R will not attempt to receive the later signal from T, even if the signal from T is stronger. This will cause the transmission on link l to fail. It is further shown in [9] that no matter how large the carrier-sensing range is, we can always come up with an example that leads to transmission failures, if the Receiver-Capture effect is not dealt with properly. This kind of collisions can be solved with a receiver RS (Re-Start) mode. In some commercial WiFi chips (e.g., the Atheros WiFi chips), the RS mode is supported. With RS mode, a receiver will switch to receive the stronger packet as long as the SINR threshold γ 0 for the later link can be satisfied. In the above example, when T transmits to R,becausethepowerfromT is much larger than the power from T, R will switch to receive the packet of T in the RS mode. In the following discussion, we also make the same assumption that the receivers are operated with the RS (Re-Start) mode.. Safe Carrier-sensing Range under Cumulative Interference Model Ref. [9] studied the safe carrier-sensing range under the pairwise interference model in the noiseless case. The threshold is given as follows: Safe-CSR pairwise = ( γ 0 α + ) d, (6) where d = d(t i,r i ) is the imum link l i L length in the network. However, the pairwise interference model does not take into account the cumulative nature of interferences from other links. The threshold given in (6) is overly optimistic and is not large enough to prevent hidden-node collisions under the cumulative interference model, as illustrated by the three-link example in Fig.. d d T d T 4d R R T R DATA DATA ACK l l Fig.. Setting the carrier-sensing range as Safe- CSR pairwise is insufficient to prevent hidden-node collisions under the cumulative interference model In Fig., suppose that the SIR requirement γ 0 = 8 and the path-loss exponent α =. According to (6), ( it is enough ) to set the carrier-sensing range as γ 0 α + d = 4d and the carriersensing power threshold P th = P t G 0 (4d ) = d l 0.056P t G 0 d. In Fig., there are three links: l, l, and l with the same link length d. The distance d(r,r ) equals d and the distance d(t,r ) equals ( 4d). Since the distance d(t,t )=4d = γ 0 α + d,from(4),wefindthatt and T can simultaneously initiate transmissions since they cannot carrier sense each other. We can verify that the SIR requirements of both DATA and ACK transmissions on l and l are satisfied. This means l and l can indeed successfully transmit simultaneously. Suppose that l wants to initiate a transmission when T is sending a DATA frame to R,andR is sending an ACK frame to T. Transmitter T senses a power P CS (T ) given by P CS (T )=P t G 0 (5d ) + P t G 0 (8d ) = P t G 0 d <P th. This means that T cannot sense the transmissions on l and l, and can therefore initiate a DATA transmission. However, when all these three links are active simultaneously, the SIR at R is P t G 0 (d ) P t G 0 (6d ) + P t G 0 (d ) =7.74 <γ 0. This means the cumulative interference powers from l and l will corrupt the DATA transmission on l due to the insufficient SIR at R. This example shows that setting the carrier-sensing range as in (6) is not sufficient to prevent collisions under the cumulative interference model. Choosing the parameters α = and γ 0 =8is just for an easy illustration. In fact, we can always construct a three-link example like Fig. with the same conclusion for any choice of α and γ 0. We next establish a threshold for Safe-CSR cumulative so that the system will remain interference safe under the cumulative interference. Conjecture : The densest packing of concurrent transmitters leads to the worst cumulative interference power at a particular receiver. Based on Conjecture, we have the following theorem: Theorem : Setting where and Safe-CSR cumulative =(K K +)d, (7) K = ( ( ) α )) α (6γ 0 +, (8) α ( K = P t G 0 P t G 0 γ 0 d α N ) α, (9) is sufficient to ensure interference-safe transmissions under the cumulative interference model. Proof: With the receiver s RS mode, in order to prevent hidden-node collisions in 80. networks, we only need to show that condition (7) is sufficient to

6 6 guarantee the satisfaction of both the SINR requirements () and () of all the concurrent transmission links. Let S CS denote a subset of links that are allowed to transmit concurrently under the Safe-CSR cumulative setting in (7). Consider any two links l i and l j in S CS, we have d(t j,t i ) Safe-CSR cumulative =(K K +)d. Because both the lengths of links l i and l j satisfy d(t i,r i ) d, d(t j,r j ) d, we have the following relationships based on the triangular inequality d(t j,r i ) d(t j,t i ) d(t i,r i ) (K K +)d, d(r j,t i ) d(t i,t j ) d(t j,r j ) (K K +)d, d(r j,r i ) d(r i,t j ) d(t j,r j ) K K d. We take the most conservative distance K K d in our interference analysis (i.e., we will pack the links that transmit concurrently in a tightest manner given the Safe-CSR cumulative in (7)). Consider any two links l i and l j in S CS. The following four inequalities are satisfied: d(t i,t j ) K K d, d(t i,r j ) K K d, d(t j,r i ) K K d, d(r i,r j ) K K d. Consider any link l i in S CS. We will show that the SINR requirements for both the DATA frame and the ACK frame can be satisfied. We first consider the SINR requirement of the DATA frame. The SINR at R i is: SINR = l j S CS,j i P t G 0 d α (T i,r i ) P t G 0 d α (S j,r i )+N. For the received signal power, we consider the worst case that d(t i,r i )=d.sowehave P t G 0 d α (T i,r i ) P t G 0 d α. (0) To calculate the worst case cumulative interference power, we consider the case that all the other concurrent transmission links have the densest packing, in which their link lengths are equal to zero. The links then degenerate to nodes. The minimum distance between any two links in S CS is K K d. The densest packing of nodes with the minimum distance requirement is the hexagon packing [] (as shown in Fig. ). If link l j is the first layer neighbor link of link l i, we have d(s j,r i ) K K d.thuswehave P t G 0 d α (S j,r i ) P t G 0 (K K d ) α = (K K ) α P t G 0 d α, and there are at most 6 neighbor links in the first layer. Fig.. The packing of interfering links in the worst case If link l j is the nth layer neighbor link of link l i with n, wehaved(s j,r i ) n K K d.thuswe have ( ) α P t G 0 d α (S j,r i ) P t G 0 nk K d = (, nk K ) α P t G 0 d α and there are at most 6n links in the nth layer. So the cumulative interference power satisfies: P t G 0 d α (S j,r i ) l j S CS,j i ( ( ) α ( ) ) α 6 + 6n P t G 0 d α K K nk K n= ( ) ( α ( ) ) α =6 + n P t G 0 d α K K n= n ( ) ( α ( ) α ( ) ) α =6 + n P t G 0 d α K K n n= ( ) ( α ( ) α ) =6 + K K n α P t G 0 d α n= ( ) α ( ( ) α ) 6 + P t G 0 d α K K α, () where () follows from a bound on Riemann s zeta function. According to (0) and (), we find that the SINR of the DATA frame of link l i at the receiver R i satisfies: SINR = l j S CS,j i ( ) α 6 K K (+ P t G 0 d α (T i,r i ) P t G 0 d α (S j,r i )+N. P t G 0 d α ( ) α α P t G 0 d α = ( ) ( ) PtG 0d α PtG γ 0 0 γ 0d α N P tg 0 + N = γ 0, ) P t G 0 d α + N ()

7 7 where () follows from the definitions of K and K as shown in (8) and (9), respectively. So the DATA frame transmission on l i can be guaranteed to be successful. The proof that the SINR requirement of the ACK frame on link l i can be satisfied follows a similar procedure as above. So condition (7) is sufficient to satisfy the SINR requirements of the successful transmissions of both the DATA and ACK frames. This means that condition (7) is sufficient for preventing hidden-node collisions in CSMA networks under the cumulative interference model. Condition (7) provides a sufficiently large carriersensing range that prevents the hidden-node collisions in CSMA networks. Therefore, there is no need to set a CSR larger than the values given in (7). Otherwise the spatial reuse will be decreased unnecessarily. The terms K and K in (7) reflect the impact of the cumulative interference power from other concurrent transmission links and the background noise power on the safe carrier-sensing range setting, respectively. So we refer to K and K as interference factor and noise factor, respectively.. The Noise Factor K The noise factor K is a function of the SNR margin (also called the noise margin). Let ρ denote the SNR margin, which can be defined as ρ = P tg 0 γ 0 d α N. The value of ρ is always no less than. In other words, the transmit power should be large enough to satisfy the SNR requirement γ 0 in the case that there is only one link in the network. The noise factor K is a function of the SNR margin: ( ) ρ α K =. ρ The term K is no less than. When the SNR margin ρ =(i.e., 0dB), the noise factor K =. Accordingto(7),wefindthatSafe-CSR cumulative =. The physical meaning is that if the transmit power P t just meets the SNR target threshold γ 0,thenitis not possible to have multiple concurrent transmitting links. Figure 4 shows the noise factor K as a function of the SNR margin ρ. Different curves represent different choices of the path-loss exponent α. From Fig. 4, we find that as the SNR margin ρ increases, the noise factor K decreases rapidly. As the SNR margin goes to infinity, the noise factor K converges to. When K =, condition (7) is simplified to Safe-CSR cumulative = (K +)d. In this case, the safe carrier-sensing range requirement is only affected by the cumulative interference power. The closer K is to, the smaller the noise power impacts on the safe carrier-sensing range requirement. In practice, the noise factor K α= α=4 α= SNR margin ρ (db) Fig. 4. The noise factor K as a function of the SNR margin 80. network operates with an SNR margin ranging from 6dB to 0dB []. From Fig. 4, we can find that the noise factor K is very close to, and the impact of the noise power to the safe carrier-sensing range requirement is small..4 The Impact of Interference Models Let us consider the impact of different interference models to the safe carrier-sensing range requirements. In order to have a clear comparison between different interference models, we set the noise power N =0. So we have Safe-CSR cumulative =(K +)d. Let us compare Safe-CSR cumulative with Safe-CSR pairwise with different values of γ 0 and α. For example, if γ 0 =0 and α =4, which are typical for wireless communications, Safe-CSR pairwise =.78 d, Safe-CSR cumulative =5.7 d. Compared with Safe-CSR pairwise, Safe-CSR cumulative needs to be increased by a factor of.4 to ensure successful transmissions under the cumulative interference model. Given a fixed path-loss exponent α, both Safe- CSR pairwise and Safe-CSR cumulative increase in the SIR requirement γ 0. This is because the separation among links must be enlarged to meet a larger SIR target. For example, if α =4,wehave ) Safe-CSR pairwise = (+γ 4 0 d, ( ( ) ) 4 Safe-CSR cumulative = + γ 4 0 d. The ratio of Safe-CSR cumulative to Safe-CSR pairwise is Safe-CSR cumulative = + ( 4 γ ) 4 0, Safe-CSR pairwise +γ 4 0

8 8 which is an increasing function of γ 0, and converges to a constant as γ 0 goes to infinity: sup γ 0 Safe-CSR cumulative Safe-CSR pairwise = lim γ 0 + ( 4 = lim γ 0 γ 0 ) 4 +γ 4 0 = ( 4 Safe-CSR cumulative Safe-CSR pairwise ) Figure 5 shows the ratio Safe-CSR cumulative Safe-CSR pairwise as a function of the SIR requirements γ 0. Different curves represent different choices of the path-loss exponent α. The ratio Safe-CSR cumulative Safe-CSR pairwise increases when γ 0 increases or α decreases. For each choice of α, the ratio converges to a constant as γ 0 goes to infinity. This shows that, compared with the pairwise interference model, the safe carrier-sensing range under the cumulative interference model will not increase unbounded. P th. A key disadvantage of this approach is that P CS (T i ) is a cumulative power from all the other nodes that are concurrently transmitting. The cumulative nature makes it impossible to tell whether P CS (T i ) is from one particular nearby transmitter or a group of far-off transmitters []. This reduces spatial reuse, as illustrated by the example in Fig. 6. l l ' T ' R R ' T The ratio Safe CSR cumulative /Safe CSR pairwise.5.5 α= α=4 α= SIR Requirement γ 0 Fig. 5. The ratio of Safe-CSR cumulative to Safe- CSR pairwise 4 A NEW CARRIER SENSING MECHANISM We now discuss the implementation of Safe- CSR cumulative. We first describe the difficulty of implementing the safe carrier-sensing range in (7) using the conventional physical carrier-sensing mechanism in 80.. Then, we propose a new Incremental-Power Carrier-Sensing (IPCS) mechanism to resolve this implementation issue. 4. Limitation of Conventional Carrier-Sensing Mechanism In the current 80. MAC protocol, given the safe carrier-sensing range Safe-CSR cumulative, the carriersensing power threshold P th can be set as P th = P t G 0 (Safe-CSR cumulative ) α. () Before transmission, a transmitter T i compares the power it senses, P CS (T i ), with the power threshold T l R R l T Fig. 6. Conventional carrier-sensing will reduce the s- patial reuse in 80. networks (Link l is placed based on the carrier-sensing mechanism in current 80., and link l is placed based on the IPCS mechanism) There are four links in Fig. 6, with Safe-CSR cumulative set as in (7). In Fig. 6, the distance d(t,t ) is equal to Safe-CSR cumulative.from(4),wefindthatt and T cannot carrier sense each other, thus they can transmit simultaneously. First, consider the location of a third concurrent transmitting link l with both l and l, assuming that each transmitter can perfectly differentiate the distances from the other transmitters. Suppose that the third link is located on the middle line between l and l. Based on the carrier-sensing range analysis, the requirements are d(t,t ) Safe-CSR cumulative and d(t,t ) Safe-CSR cumulative. So the third link can be located in the position of l, shown in Fig. 6. Furthermore, as the number of links increases, a tight packing of the concurrent transmitters will result in a regular equilateral triangle packing with side length Safe-CSR cumulative. The consumed area of each transmitter is a constant given by A = Safe-CSR cumulative. Now, let us consider the location requirement of the third link l under the carrier-sensing mechanism of the current 80. protocol. In order to have concurrent transmissions with both l and l, the cumulative power sensed by T due to transmissions of both links l and l should be no larger than P th, i.e., P CS (T )=P t G 0 d(t,t ) α + P t G 0 d(t,t ) α = P t G 0 d(t,t ) α P th,

9 9 where P th is given in equation (). So the minimum distance requirement on d(t,t ) and d(t,t ) is ( d(t,t )=d(t,t ) P ) α t P th = α Safe-CSR cumulative, as shown in Fig. 6. Since α is always greater than for any choice of α, the requirement of the separation between transmitters is increased from Safe-CSR cumulative (i.e., d(t,t )) to α Safe-CSRcumulative (i.e., d(t,t ) and d(t,t )). The requirement on the separation between transmitters will increase progressively as the number of concurrent links increases, and the corresponding packing of transmitters will be more and more sparse. As a result, spatial reuse is reduced as the number of links increases. Another observation is that the transmissions order (i.e., which link transmits first and which link transmits next) also affects spatial reuse in the conventional carrier-sensing mechanism. Consider the three links, l, l and l in Fig. 6 again. If transmissions order is {l,l,l }, as discussed above, T, T and T sense a power no greater than P th, and thus l, l and l can be active simultaneously. If the sequence of transmissions on these links is {l,l,l }, however, both T and T senseapowernolargerthanp th.but the cumulative power sensed by T in this case is P CS (T )=P t G 0 d(t,t ) α + P t G 0 d(t,t ) α ( ( =P t G ) ) α α 0 + = P th >P th. Safe-CSR α cumulative Therefore, T will sense the channel busy and will not initiate the transmission on l. The spatial reuse is further reduced because there would have been no collisions had T decided to transmit. 4. Incremental-Power Carrier-Sensing (IPCS) Mechanism We propose a novel carrier-sensing mechanism called Incremental-Power Carrier-Sensing (IPCS) to solve the issues identified in Section 4.. Specifically, the IPCS mechanism can implement the safe carrier-sensing range accurately by separating the detected powers from multiple concurrent transmitters. Before explaining the details of IPCS, we want to emphasize that there are two fundamental causes for collisions in a CSMA network. Besides hidden nodes, collisions can also happen when the backoff mechanisms of two transmitters count down to zero simultaneously, causing them to transmit together. Note that for the latter, each of the two transmitters. This corresponds to the exposed-node phenomenon. is not aware that the other transmitter will begin transmission at the same time. Based on the power that it detects, it could perfectly be safe for it to transmit together with the existing active transmitters, only if the other transmitter did not decide to join in at the same time. There is no way for the carriersensing mechanism to prevent this kind of collisions. This paper addresses the hidden-node phenomenon only. To isolate the second kind of collisions, we will assume in the following discussion of IPCS that no two transmitters will transmit simultaneous due to simultaneous backoff countdown-to-zero. Conceptually, we could imagine the random variable associated with backoff countdown to be continuous rather than discrete, which means that the starting/ending of one link s transmission will coincide with the starting/ending of another link s transmission with zero probability. The case of discrete backoff time will be treated in Section 6.. In particular, we argue that IPCS remains hidden-node-free with the same carriersensing power threshold in () when the backoff time is discrete. Algorithm : Incremental-Power Carrier-Sensing (IPCS) Input: Pi CS (t): thepowersensedbyt i Output: channel status decision Monitor every increment ΔPi CS (t k ) during time window [t t packet,t]; if ΔPi CS (t k ) P th, t k such that t t packet t k t, then T i decides that the channel is idle at time t; 4 else 5 T i decides that the channel is busy at time t; 6 end The IPCS mechanism is described in Algorithm. The key idea of IPCS is to utilize the whole carriersensing power history, not just the carrier-sensing power at one particular time instance. In CSMA networks, each transmitter T i carrier senses the channel except during its transmission of DATA or reception of ACK. The power being sensed increases if a new link starts to transmit, and decreases if an active link finishes its transmission. As a result, the power sensed (t), is a function of time t. In IPCS, instead of checking the absolute power sensed at time t, the transmitter checks increments of power in the past up to time t. If the pack- by transmitter T i, denoted by P CS i et duration t packet (including both DATA and ACK frames and the SIFS in between) is the same for all links, then it suffices to check the power increments during the time window [t t packet,t]. The same packet duration assumption is used to simplify explanation only. For the general case in which different packets have different packet length-

10 0 s, we could check a sufficiently large time window to cover the imum packet size among all links. Let {t,t,,t k, } denote the time instances when the power being sensed changes, and {ΔPi CS (t ), ΔPi CS (t ),, ΔPi CS (t k ), } denote the corresponding increments, respectively. In IPCS, transmitter T i considers the channel to be idle at time t if the following conditions are met: ΔPi CS (t k ) P th, t k such that t t packet t k t, (4) where P th is the carrier-sensing power threshold determined according to CSR; otherwise, the channel is considered to be busy. SinceΔPi CS (t k ) is negative if a link stops transmission at some time t k,weonlyneed to check the instances where the power increments are positive. By checking every increment in the detected power over time, T i can separate the powers from all concurrent transmitters, and can map the power profile to the required distance information. In this way, IPCS can ensure the separations between any two transmitters of all the transmitters are tight in accordance with Theorem. Theorem : If the carrier-sensing range is set as equation (7), and the carrier-sensing power threshold P th in the IPCS mechanism is set as equation (), then it is sufficient to prevent hidden-node collisions under the cumulative interference model. Proof: Consider any link l i in set L. Transmitter T i will always do carrier sensing except when it transmits DATA frame or receives ACK frame. We show that condition () is sufficient to prevent hiddennode collisions in the following two situations, which cover all the possible transmission scenarios: ) Link l i has monitored the channel for at least t packet length of time before its backoff counter reaches zero and it transmits. ) Link l i finishes a transmission; then monitors the channel for less than t packet when its backoff counter reaches zero; then it transmits its next packet. Let us first consider case ): We show that for the links that are allowed to transmit simultaneously, the separation between any pair of transmitters is no less than the safe carrier-sensing range Safe-CSR cumulative. We prove this through induction. Suppose that before l i starts to transmit, there are already M links transmitting and they are collectively denoted by the link set S CS. Without loss of generality, suppose that these M links begin to transmit one by one, according to the order l,l,,l M.For. For the case in which the packet lengths are different, setting the time window that to the imum packet size may be overly conservative and not efficient for small packets. To improve efficiency, we further propose Incremental-and-Decremental- Power Carrier-Sensing (IDPCS), which monitors both increments and decrements to make carrier sensing decision. The details of IDPCS are in Section 6.. any link l j S CS,lett j and t j denote the times when link l j starts to transmit the DATA frame and the ACK frame, respectively. In our inductive proof, by assumption we have d(t j,t k ) Safe-CSR cumulative, j, k {,,M},j k. (5) We now show that condition (5) will still hold after link l i starts its transmission. Before link l i starts its transmission, transmitter T i monitors the channel for a time period of t packet.so T i at least senses M increments in the carrier-sensing power Pi CS (t) that happen at time t,t,,t M when the links in S CS start to transmit their DATA frames. There may also be some increments in the Pi CS (t) that happen at t,t,,t M if the links in SCS start to transmit the ACK frames before link l i starting it transmission. In the IPCS mechanism, at least the following M inequalities must be satisfied if T i can start its transmission: Because we have ΔP CS i (t j ) P th, for j =,,M. (6) ΔP CS i (t j )=P t G 0 d(t i,t j ) α, (7) P th = P t G 0 (Safe-CSR cumulative ) α, d(t i,t j ) Safe-CSR cumulative for j =,,M. (8) Thus, we have shown that the separation between any pair of transmitters in the set S CS l i is no less than Safe-CSR cumulative after link l i starting transmission. Now let us consider case ): Before starting the transmission of the (m +)th packet, link l i first finishes the transmission of the mth packet (from time t i (m) to t i (m) +t packet ), and waits for a DIFS plus a backoff time (from time t i (m)+ t packet to t i (m+)). Let S CS denote the set of links that are transmitting when l i starts the (m +)th packet at time t i (m +). Consider any link l j in set S CS. Because the transmission time of every packet in the network is t packet. We know that the start time t j of the concurrent transmission on link l j must range from t i (m) to t i (m +), i.e., t i (m) <t j <t i (m +). If t i (m)+t packet <t j <t i (m+), this means t j is in thedifsorthebackofftimeoflinkl i.duringthisperiod, transmitter T i will do carrier sensing. The IPCS mechanism will make sure that the distance between T i and T j satisfies d(t i,t j ) Safe-CSR cumulative. If t i (m) <t j <t i (m)+t packet, this means t j falls into the transmission time of the mth packet of link l i.during the transmission time, T i is not able to do carrier sensing because it is in the process of transmitting the DATA frame or receiving the ACK frame. However, the transmitter T j will do carrier sensing before it starts to transmit at time t j. The carrier sensing done

11 by T j can make sure that the distance between T i and T j satisfies d(t i,t j ) Safe-CSR cumulative. So for any link l j in S CS, we have d(t i,t j ) Safe-CSR cumulative. Let us use Fig. 6 again to show how IPCS can implement the safe carrier-sensing range successfully. We set the carrier-sensing power threshold P th as in (). We will show that the location requirement of the third link under IPCS is the same as indicated by the safe carrier-sensing range (location l in Fig. 6). P CS P CS P () t ( t ) ( t ) CS t t Fig. 7. The power sensed by transmitter T as a function of time The transmitter of the third link will only initiate its transmission when it senses the channel to be idle. Its carrier-sensed power is shown in Fig. 7. Without loss of generality, suppose that link l starts transmission before l. The third transmitter detects two increments in its carrier-sensed power at time instances t and t which are due to the transmissions of T and T, respectively. In the IPCS mechanism, the third transmitter will believe that the channel is idle (i.e., it can start a new transmission) if the following is true: { ΔP CS (t )=P t G 0 d(t,t ) α P th, ΔP CS (t )=P t G 0 d(t,t ) α (9) P th. Substituting P th in () to (9), we find that the requirements in (9) are equivalent to the following distance requirements: { d(t,t ) Safe-CSR cumulative, d(t,t ) Safe-CSR cumulative. So the third link can be located at the position of l,as shown in Fig. 6, instead of far away at the location of l as in the conventional carrier-sensing mechanism. Compared with the conventional carrier-sensing mechanism, the advantages of IPCS are ) IPCS is a pairwise carrier-sensing mechanism. In the IPCS mechanism, the power from each concurrent link is checked individually. This is equivalent to checking the separation between every pair of concurrent transmission links. With IPCS, all the analyses based on the concept of a carrier-sensing range remain valid. ) IPCS improves spatial reuse and network throughput. In the conventional carrier-sensing mechanism, the link separation requirement increases as the number of concurrent links increases. In IPCS, however, the link separation t requirement remains the same. Furthermore, because IPCS is a pairwise mechanism, the order of the transmissions of links will not affect the spatial reuse. 5 SIMULATIONS RESULTS We perform simulations to evaluate the throughput performance of IPCS compared to the conventional Carrier Sensing (CS). In our simulations, the nodes are located within a square area of 00m 00m. The locations of the transmitters are generated according to a Poisson point process. The link length ranges from 0m to 0m. More specifically, the receiver associated with a transmitter is randomly located between the two concentric circles of radii 0m and 0m centered on the transmitter. We study the system performance under different link densities and carriersensing power thresholds. For each given number of links, we investigate 00 random network topologies and present the averaged results. The simulations are carried out based on the 80.b protocol. The carrier frequency is.4ghz.the bandwidth is 0MHz. The reference channel gain G 0 at the reference distance d 0 = m and the carrier frequency of.4ghz is 4.9dB [4]. The common physical layer link rate is Mbps. The packet size is 460 Bytes. The minimum and imum backoff windows and CW are and 0, respectively. The backoff time of each transmitter is uniformly distributed between CW min and CW. The slot time length is 0μs. TheSIFSandDIFSare0μs and 50μs, respectively. The transmit power P t is set as 00mW. The noise power density is 74dBm/Hz. Thepath- loss exponent α is 4, the SINR requirement γ 0 is 0. We first investigate the spatial reuse and network throughput performances under different link densities, by varying the number of links in the square from to 00 in our simulations. The carrier-sensing range and the carrier-sensing power threshold are set according to (7) and (), respectively. In particular, Safe- CSR cumulative = 7.6m and P th = mw with the system parameters assumed. Simulation results show that the network throughput is proportional to spatial reuse. So we plot these two results together in Fig. 8. We define a unit area as the consumed area of each active transmitter under the tightest packing. Given Safe-CSR cumulative = 7.6m, the unit area is Safe-CSR cumulative =. 04 m. The x-axis is the average number of links (i.e., all active and inactive links) per unit area as we vary the total number of links in the whole square. That is, the x-axis corresponds to the link density of the network. The left y- axis is the spatial reuse, or the average active link density in the network. The imum value of the spatial reuse is, which is shown as a dashed line

12 spatial reuse IPCS Conventional CS theorectical result (optimal) average number of links per unit area Fig. 8. Spatial reuse and network throughput under IPCS and the conventional CS mechanism as a function of network density in Fig. 8. The right y-axis is the throughput per unit area. It is clear from Fig. 8 that IPCS outperforms the conventional CS. The improvement becomes more significant when the network becomes denser. At the densest point in the figure, spatial reuses under IPCS and conventional CS are and 0.584, respectively. The network throughputs per unit area are 6.66Mbps and 4.08Mbps, respectively. Using conventional CS as the base line, the IPCS improves spatial reuse and network throughput by up to 60%. Under the conventional CS, in order to make sure the cumulative detected power is no larger than the power threshold P th, the packing of concurrent transmission links will become more and more sparse as additional number of links attempt to transmit. Under IPCS, this does not occur. As a result, the improvement in spatial reuse is more significant as the network becomes denser. We also find that when the network becomes denser and denser, spatial reuse under IPCS becomes very close to the theoretical imum result. The small gap is likely due to the fact that a link which could be active concurrently under IPCS does not exist in a given topology. The probability of this happening decreases as the network becomes denser. Figure 9 shows the network throughput performance of IPCS and the conventional CS mechanism under different carrier-sensing power thresholds. The number of links in the square is fixed at 00 (and thus the average number of links per unit area is 6.67). At the initial point, the carrier-sensing power threshold P th is set according to (), which is mw. Because the simulations are performed within a finitesize network, setting the carrier-sensing power according to () is sufficient but may also be too conservative to prevent collisions. Then we increase throughput per unit area (Mbps) throughput per unit area (Mbps) collision happens under IPCS IPCS Conventional CS collision happens under Conventional CS carrier sensing power threshold (mw) x 0 8 Fig. 9. Network throughput under IPCS and the conventional CS mechanism as a function of the carriersensing power threshold P th in each mechanism, until collisions just happen and the mechanism fails to prevent them. Therefore, this means that the transmissions are interference-safe for all values points we plotted in Fig. 9. Since IPCS monitors incremental power and the conventional CS monitors the total power, IPCS first incur collisions at a smaller P th than the conventional CS (i.e., at the same P th, IPCS allows more links to transmit simultaneously). It is clear from Fig. 9 that IPCS outperforms the conventional CS as we vary the carrier-sensing power threshold. Using the conventional CS as the base line, the throughput improvement of IPCS is more than 50% under the same carrier-sensing power thresholds. If we compare the imum throughput obtained in IPCS to the imum throughput obtained in the conventional CS in the interference-free regime, the throughput improvement of IPCS is still more than 5%. 6 FURTHER DISCUSSIONS In this section, we will discuss two issues: the first one is the IPCS mechanism when the backoff time is a discrete random variable; the second one is how to improve the transmission efficiency of IPCS when the packet lengths are different. 6. IPCS With Discrete Backoff Time For simplicity, we have assumed a continuous backoff time when discussing the main characteristic of the IPCS mechanism in this paper. In fact, Theorem remains valid even if we remove the continuous backoff time assumption. In other words, IPCS can still prevent hidden-node collisions even when the backoff time is a discrete random variable. We remark, however, that with discrete backoff time, it is possible for multiple transmitters to count down to zero and transmit simultaneously. These collisions are not due to hidden nodes and will always be present so long

13 as the countdown process is discrete, and they are not the subject of focus of this paper. Consider some time instance t, when the transmitter T i senses an increment power composed of the sum of the powers from H, (H ) concurrent transmitters (denoted as T jh,h =,,H), due to their discrete backoff counters reaching zero simultaneously. Then (6) and (7) in the proof of Theorem become and ΔP CS i (t) = ΔP CS i (t) P th, (0) H P t G 0 d(t i,t jh ) α. () h= The carrier-sensing power threshold P th is P t G 0 (Safe-CSR cumulative ) α. Then we have H P t G 0 d(t i,t jh ) α P t G 0 (Safe-CSR cumulative ) α. h= Therefore, d(t i,t jh ) Safe-CSR cumulative for h =,,H. This means that the safe carrier-sensing range requirement (8) in the proof of Theorem is still satisfied. If the carrier-sensing power threshold is set as (), IPCS can prevent hidden-node collisions whether the backoff time is a continuous random variable or a discrete random variable. We do note, however, that IPCS will be more conservative when the backoff time is discrete. When multiple transmitters count down to zero and transmit simultaneously, the sensing node treat their powers as the power coming from one single transmitter that is closer to the sensing node. Thus, the sensing node may withhold transmission even though it may be safe to transmit. However, under no circumstance will the sensing node transmit when it is not safe to do so. 6. IDPCS Mechanism When the packet lengths are different, setting the time window to the imum packet size may be overly-conservative. In IPCS, if an increment in the detected power is larger than the power threshold P th, the transmitter T i will freeze for a time duration which is equal to the imum packet length. If this increment is caused by a small packet, such long freeze time is not necessary. In order to improve the transmission efficiency, we propose the IDPCS mechanism which monitors power decrements in addition to power increments. The IDPCS mechanism is given in Algorithm. In IDPCS, T i maintains a counter, which is the number of concurrent transmissions with the detected power increments larger than the power threshold P th. Whenever T i detects a power increment larger than P th, the counter is increased by, because a new Algorithm : Incremental-and-Decremental-Power Carrier-Sensing (IDPCS) Input: Pi CS (t): thepowersensedbyt i Output: channel status decision counter 0; Monitor every change ΔPi CS (t k ) in the detected power; if ΔPi CS (t k ) P th, then 4 counter ++; 5 end 6 if ΔPi CS (t k ) P th, and counter > 0 then 7 counter ; 8 end 9 if counter == 0 at time t, then 0 T i decides that the channel is idle at time t; else T i decides that the channel is busy at time t; end transmission (DATA frame or ACK frame) within the carrier-sensing range has begun. If T i detects a power decrement which is greater than P th, this means that a link within the carrier-sensing range has finished its transmission (DATA frame or ACK frame). In this case, the counter is decreased by. If the counter is zero, this means there is no link in the carrier-sensing range that is transmitting. Then the transmitter T i decides the channel to by idle; otherwise, the channel is considered to be busy. By monitoring both increments and decrements, the transmitter can track both the start and the end of each transmission. A transmitter does not need to freeze for the imum packet length once it detects an increment in the detected power that is larger than P th. This will improve the transmission efficiency. 7 CONCLUSION In this paper, we derive a threshold on the safe carriersensing range that is sufficient to prevent hidden-node collisions under the cumulative interference model. We then propose a novel carrier-sensing mechanism, called Incremental-Power Carrier-Sensing (IPCS), that can realize the safe carrier-sensing range concept in a simple way. The IPCS checks every increment in the detected power so that it can separate the detected power of every concurrent transmitter, and then maps the power profile to the required distance information. Our simulation results show that IPCS can boost spatial reuse and network throughput by up to 60% relative to the conventional carrier-sensing mechanism under the same carrier-sensing power thresholds. If we compare the imum throughput in the interference-free regime, the throughput improvement of IPCS is still more than 5%. Last but not least, by providing an explicit implementation

14 4 of the concept of carrier-sensing range, IPCS also ties up a loose end in many other prior theoretical works that implicitly assume the use of a carriersensing range (interference-safe or otherwise) without an explicit design to realize it. One future research direction is to study the interference-safe transmissions in CSMA networks while considering the fading and time-varying effects of the wireless channel. In this paper, we only consider the log-distance path model. Channel fading will influence both the detected powers by transmitters and the interference powers at the receivers. It requires a probabilistic analysis approach which is quite d- ifferent from the deterministic approach used here. The carrier-sensing design to avoid severe interference under fast fading is an interesting topic for future study. REFERENCES [] L. Fu, S. C. Liew, and J. Huang, Effective carrier sensing in CSMA networks under cumulative interference, in Proc. IEEE INFOCOM, Mar. 00. [] G. Brar, D. 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Mag., vol. 9, no. 6, pp. 0 7, Jun. 00. [6] L.Fu,S.C.Liew,andJ.Huang, Safecarriersensingrangein CSMA network under physical interference model, Technical Report, [7] C. K. Chau, M. Chen, and S. C. Liew, Capacity of large-scale CSMA wireless networks, in Proc. ACM MOBICOM, 009. [8] T. S. Kim, H. Lim, and J. C. Hou, Improving spatial reuse through tuning transmit power, carrier sense threshold, and data rate in multihop wireless networks, in Proc. ACM MO- BICOM, 006. [9] T. Y. Lin and J. C. Hou, Interplay of spatial reuse and SINRdetermined data rates in CSMA/CA-based, multi-hop, multirate wireless networks, in Proc. IEEE INFOCOM, 007. [0] T. S. Rappaport, Wireless Communications: Principles and practice, nd ed. Prentice Hall PTR, 00. [] C. A. Rogers, Packing and Covering. Cambridge University Press, 964. [] [Online]. Available: pa0hoo/helix wifi/linkbudgetcalc/wlan budgetcalc.html. [] K. Jamieson, B. Hull, A. Miu, and H. Balakrishnan, Understanding the real-world performance of carrier sense, in ACM SIGCOMM Workshops, 005. [4] M. S. Gast, 80. Wireless Networks: The Definitive Guide, nd ed. O Reilly Media Inc., 005. Liqun Fu (S 08-M ) is currently a postdoctoral fellow with the Institute of Network Coding at The Chinese University of Hong Kong. She received the Ph.D. Degree in Information Engineering from The Chinese University of Hong Kong in 00. She worked as a visiting research student in the Department of Electrical Engineering, Princeton University from June to November, 009. Her current research interests are in the area of wireless communications and networking, with focus on wireless greening, resource allocation, distributed protocol design, and physical-layer network coding. Soung Chang Liew (S 87-M 88-SM 9-F ) received the Ph.D. degree from the Massachusetts Institute of Technology (MIT), Cambridge, in 988. From March 988 to July 99, he was with Bellcore (now Telcordia), Piscataway, NJ. He has been a Professor with the Department of Information Engineering, the Chinese University of Hong Kong since 99. His research interests include wireless communications and networking, Internet protocols, multimedia communications, and packet switch design. Prof. Liew is a Fellow of IEEE, IET and HKIE. Jianwei Huang (S 0-M 06-SM ) is an Assistant Professor in the Department of Information Engineering at the Chinese University of Hong Kong. He received Ph.D. from Northwestern University (Evanston, IL) in 005, and worked as a Postdoc Research Associate in Princeton University during Dr. Huang leads the Network Communications and Economics Lab (ncel.ie.cuhk.edu.hk), with main research focus on nonlinear optimization and game theoretical analysis of communication networks. He is the recipient of the IEEE Marconi Prize Paper Award in Wireless Communications in 0, the ICST WiCON Best Paper Award 0, the IEEE GLOBE- COM Best Paper Award in 00, the IEEE ComSoc Asia-Pacific Outstanding Young Researcher Award in 009, APCC Best Paper Award in 009. He serves as the Editor of IEEE Journal on Selected Areas in Communications - Cognitive Radio Series and Editor of IEEE Transactions on Wireless Communications.